A meteorologist predicts the probability of rain on Monday is , on Tuesday is , and on Wednesday is . Assuming the weather on each day is independent, what is the probability of rain on all three days?
Options
A
B
C
D
Answer & Analysis
Answer
C
Analysis
Question Analysis
This question involves calculating the joint probability of three independent weather events (rain on consecutive days).
The main focus is on applying the multiplication rule for independent events, where the occurrence of rain on one day does not affect other days.
Key Concept Explanation
For independent events, the probability of all events occurring is the product of their individual probabilities:
Each day’s weather is independent, so we multiply the probabilities of rain on Monday, Tuesday, and Wednesday.
Step-by-Step Solution
1. List the individual probabilities:
,
,
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